Finite Group DatabasebetaFinite Group DatabasebetaOrder 9088.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D71 |
| commutator | C2×C4×C71 | C24 |
| Frattini | C2×C4 | C23×D71 |
| Fitting | #496×C71 | C2 |
| socle | C22×C71 | C22×D4 |
| hypercenter | #496 | D71 |
| hypocenter | C71 | #3153 |
| LCS | G ▷ C2×C4×C71 ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #496 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14556157 | C2 | semidirect |
| 2. C2×#14556152 | C2 | semidirect |
| 3. #17986547 | C2 | semidirect |
| 4. #124×D71 | C2 | semidirect |
| 5. #17986394 | C2 | semidirect |
| 6. #17986393 | C2 | semidirect |
| 7. #17986386 | C2 | semidirect |
| 8. #17986382 | C2 | semidirect |
| 9. #17986380 | C2 | semidirect |
| 10. #17985951 | C2 | semidirect |
| 11. #496×C71 | C2 | semidirect |
| 17. C2×Dic284 | C22 | semidirect |
| 18. C2×#11765855 | C22 | semidirect |
| 21. C2×#11765853 | C22 | semidirect |
| 24. #14556128 | C22 | semidirect |
| 28. #14556115 | C22 | semidirect |
| 34. #14556039 | C22 | semidirect |
| 35. C8×Dic71 | C22 | semidirect |
| 36. C2×SD16×C71 | C22 | semidirect |
| 38. #127×C71 | C22 | semidirect |
| 40. #97×C71 | C22 | semidirect |
| 62. #11765848 | D4 | semidirect |
| 135. C71 | #3153 | semidirect |
| 143. #496 | D71 | semidirect |
| 157. C2×SD16 | C2×D71 | semidirect |
| 162. #127 | C2×D71 | semidirect |
| 174. #97 | C2×D71 | semidirect |